Better resolution is not necessarily a good thing if that resolution is based on errors in the data - it's essentially pseudo-precision. Partial deletion looks for any sites that are present in any pair of sequences, while "use all sites" is going to treat the absence of data as a character. There's also the option of complete deletion will eliminate any sites with data missing, whether sequencing errors or gaps. Which of these you'll want to use will depend at least partially on the analysis method you're using. In an MP analysis if the "missing data" that is caused by sequencing errors is treated as data, then you will introduce a lot of erroneous changes and this will cause serious problems with the phylogeny. It's never a good idea to include "gapped" data in an MP analysis unless you're coding gaps as presence absence characters separate from the sequence - otherwise it will treat each site within the gap as a separate mutational event. That will introduce falsely long branches and bogus statistical support in a Bootstrap analysis (PAUP* had an option to not treat gaps as data, but Mega doesn't seem to have that option). ML and NJ should be less sensitive to all of these problems since they use distances to calculate the topology and branch lengths rather than synapomorphies, but that also means that you can safely use pairwise deletion without losing a lot of data.

You seem confident that some of your alignment gaps are good data rather than sequencing errors (which seems odd for CO1, which is so conserved, but I guess it depends on how distant your taxa are from each other). If you want to preserve those and the sequencing errors are concentrated towards the ends of your sequences you may be better off trimming down the alignment to the regions that have coverage in the majority of your sequences. You can do that by brute force just deleting data, or Mega will let you define domains to be used in the analysis and you can just define the region(s) you want to use. Once you've eliminated questionable regions you can be a bit more confident about using "use all sites", although I still wouldn't use that for MP analysis.

It seems you have determined that the partial deletion feature introduces a bad artifact into your phylogenetic analysis - so you probably want to use all sites (this is what I would recommend in general anyway). I would also recommend trying a bayesian analysis in something like MrBayes or BEAST, which is very easy to do with a single gene dataset like yours. Generally, if you are getting the same tree using methods that have very different assumptions, this indicates higher support for the actual signal in your data, regardless of what the bootstrap supports or posterior probabilities tell you. Using the partial deletion method might actually be dropping alot of 'good' data from your alignment - in general I think it's better to use all of the data you have, and to just honestly describe your dataset in the results section of your subsequent publications. It's ok to have a gappy alignment, as long as you are upfront about that - the data is what the data is. It's never going to be perfect, even with whole genomes! 

Better resolution is not necessarily a good thing if that resolution is based on errors in the data - it's essentially pseudo-precision. Partial deletion looks for any sites that are present in any pair of sequences, while "use all sites" is going to treat the absence of data as a character. There's also the option of complete deletion will eliminate any sites with data missing, whether sequencing errors or gaps. Which of these you'll want to use will depend at least partially on the analysis method you're using. In an MP analysis if the "missing data" that is caused by sequencing errors is treated as data, then you will introduce a lot of erroneous changes and this will cause serious problems with the phylogeny. It's never a good idea to include "gapped" data in an MP analysis unless you're coding gaps as presence absence characters separate from the sequence - otherwise it will treat each site within the gap as a separate mutational event. That will introduce falsely long branches and bogus statistical support in a Bootstrap analysis (PAUP* had an option to not treat gaps as data, but Mega doesn't seem to have that option). ML and NJ should be less sensitive to all of these problems since they use distances to calculate the topology and branch lengths rather than synapomorphies, but that also means that you can safely use pairwise deletion without losing a lot of data.

You seem confident that some of your alignment gaps are good data rather than sequencing errors (which seems odd for CO1, which is so conserved, but I guess it depends on how distant your taxa are from each other). If you want to preserve those and the sequencing errors are concentrated towards the ends of your sequences you may be better off trimming down the alignment to the regions that have coverage in the majority of your sequences. You can do that by brute force just deleting data, or Mega will let you define domains to be used in the analysis and you can just define the region(s) you want to use. Once you've eliminated questionable regions you can be a bit more confident about using "use all sites", although I still wouldn't use that for MP analysis.

For MP analysis, Laura's comments are absolutely correct - but you should definitely not just rely on MP to make your inference. It's by far the most easily misled inference method.AFAIK  It is not correct that likelihood methods treat gaps as characters- unless this is explicitlly modeled. The standard GTR family of models treat all gaps as missing data, and those sites just don't contribute to the solution.

Both comment are vorrect and not in a sense that better the allignment is better the tree that you can have keep aldo in mind that after sllign to have done the manusl editing to have again the protein format lost after the allignment this normally means to remove gaps etc etc

MP suffered of the long branch actaction and ML one time choose the bedt evolutionary model by jmodel test have the bootstrsp anslysis as a sort of ststistic methods but bootstrapping is an iteration not a true statistic whereas bayesian methods ude a real probability 

anyway make the allignment after manusl editing remove gaps choose the evolutionary model and run bates ir beast

Thanks all! These answers have made things significantly clearer for me. Thank you a million times over!

Maybe a reminder about the basics:

generally, phylogenetic reasoning is about comparison of homologous characters. For molecular evolution, this is based on CORRECT alignments in which HOMOLOGOUS bases are place on top of each other.

If you spoiled the alignment, because partially you aligned non-homolgous sites, it is nearly unpredictable "how much error" you introduce. If reconstructed trees differ a lot, depending on more or less integration of dubiously aligned sites through the "pairwise full seq comparison" options, this is a bad sign ...

Choice of tree reconstruction methods is probably secondary then. If the data basis (alignment) is screwed up, it might be that two good methods converge on the wrong solution. "Majority votes" do not generally add confidence (in this regard I disagree with another comment posted).

Sometime one needs to conclude that the data are insufficient to draw conclusions.

Thank you Eike! I completely understand that the alignment is a crucial step and we ultimately decided that the large gaps were messing our alignments up. So we have cut each sequence down to that of the shortest ones and removed any 'spotty' sequences. This allowed us to align with more confidence and negated the 'treat,ent of gaps/missing data' issue.

One way to improve an alignment of protein-coding sequences is to translate to protein and then back. This will partially take care of the gaps, because any gaps that break up the codons are erroneous.

Sorry, one more thought: how closely related are your taxa? If rather divergent, then CoI is not a good marker anyway (too much saturation). If they are closely related, then using curated sequences from other related taxa, available on GenBank or BOLD, may be a good guidance. You can see if your sequences differ widely from published ones.

Another useful thing for fast-evolving mitochondria markers is to partitions the CDS by codon position: the third position is often very saturated and messes up likelihood/Bayesian inference (see Brandley et al. SysBio 2011).