id like to know the similarities and differences of using morphological data vs molecular data for compiling a data matrix and conducting a phylogenetic analysis
The major difference lies in the space of possible states and in the number of relevant levels of granularity and frames of reference. Whereas in molecular data at the nucleotide level the space is limited to only 4 different states (the 4 different nucleotide types), in morphology there is practically no such limitation. Moreover, whereas in molecular data you usually analyse the data either on the granularity level of individual nucleotides or on the level of amino acids. Different frames of reference are usually not used, but sometimes gene arrangement and 3d structure is also considered. In morphology, all different kinds of levels of granularity are considered, from the molecular level to the gross anatomy level. Moreover, different frames of reference can be considered, as for instance a purely spatio-structureal frame as opposed to a functional or a developmental frame.
All this affects the descriptive level as well as the analytical level in phylogenetic investigations. Molecular data can usually be described as a sequence of letters using a 4-letter code. This lends itself to very formalized descriptions of sequences. In morphology, we are dealing with a lack of such formalism. Instead, we are facing different terminological traditions that are often taxon-dependent, where the meaning of terms can vary between different authors and through time and where also homology considerations influenced terminology. No formalized standard exists for morphological descriptions.
In the step of character identification and homology assessment, using molecular data we must align sequences and then each nucleotide position in the sequence is a putative phylogenetic character with a set of 4 different possible character states. This can be easily formalized for phylogenetic algorithms to analyze the data. This is straight forward. In morphology, this step is tricky due to the space of possible states. The delimitation of characters is non-trivial and the different levels of granularity and frames of reference make it even more complicated. We have discussed these differences between morphological and molecular data in some detail in our 'The Linguistic Problem of Morphology' paper (https://www.researchgate.net/publication/215827731_The_linguistic_problem_of_morphology_Structure_versus_homology_and_the_standardization_of_morphological_data).
We are currently working on a solution for formalizing morphological descriptions using ontologies and semantic technology
The major difference lies in the space of possible states and in the number of relevant levels of granularity and frames of reference. Whereas in molecular data at the nucleotide level the space is limited to only 4 different states (the 4 different nucleotide types), in morphology there is practically no such limitation. Moreover, whereas in molecular data you usually analyse the data either on the granularity level of individual nucleotides or on the level of amino acids. Different frames of reference are usually not used, but sometimes gene arrangement and 3d structure is also considered. In morphology, all different kinds of levels of granularity are considered, from the molecular level to the gross anatomy level. Moreover, different frames of reference can be considered, as for instance a purely spatio-structureal frame as opposed to a functional or a developmental frame.
All this affects the descriptive level as well as the analytical level in phylogenetic investigations. Molecular data can usually be described as a sequence of letters using a 4-letter code. This lends itself to very formalized descriptions of sequences. In morphology, we are dealing with a lack of such formalism. Instead, we are facing different terminological traditions that are often taxon-dependent, where the meaning of terms can vary between different authors and through time and where also homology considerations influenced terminology. No formalized standard exists for morphological descriptions.
In the step of character identification and homology assessment, using molecular data we must align sequences and then each nucleotide position in the sequence is a putative phylogenetic character with a set of 4 different possible character states. This can be easily formalized for phylogenetic algorithms to analyze the data. This is straight forward. In morphology, this step is tricky due to the space of possible states. The delimitation of characters is non-trivial and the different levels of granularity and frames of reference make it even more complicated. We have discussed these differences between morphological and molecular data in some detail in our 'The Linguistic Problem of Morphology' paper (https://www.researchgate.net/publication/215827731_The_linguistic_problem_of_morphology_Structure_versus_homology_and_the_standardization_of_morphological_data).
We are currently working on a solution for formalizing morphological descriptions using ontologies and semantic technology
There is not much one can add to Lars Vogt´s thorough answer. Molecular characters need not be defined specifically, they are one of 4 states, unless you want to perform higher-order "molecular morphology". In Morphological data, character definition on the other hand matters a lot, and the definition of each character used needs to be carefully assessed. Imho, a morphological character is anything you can define as such, but few may be valuable for phylogenetic reconstruction, and deciding beforehand, which state is ancestral or derived easily introduces circular logic.
Also, molecular data in comparison to morphological data, lends itself more to distance-based methods of analysis, instead of parsimony-based methods of reconstruction. Whereas in Morphology, character state definition is in my opinion the most crucial step, on which much of the results depends, in molecular data it is the statistical, algorithm-based treatment of the raw data, e.g., choice of a suitable evolution model, model test method, alignment and so forth, that may severly impact the result
Beyond the above points in which I mostly agree, it's a matter of interpretation and focus of your research. It will depend if you are more interested in exploring phylogenetic tendencies or more regional/local patterns, for which morphology might provide more information by being combined with environmental data.