I think both native proteins and peptides are used to produce antibodies, depending upon the protein and its complexity, the species the protein comes from vs species in which antibody is made, etc. Breaking down your question:

T cells are stimulated by peptide-loaded MHC molecules. Native proteins can be processed by antigen presenting cells (APCs), like dendritic cells, into peptides of necessary length. Any stimulation of T cells you get as a result of exposure to these APCs is likely a polyclonal immune response to the protein you used.

However, you cannot control where in the protein you would get the reaction - if you have a specific area of your protein that you are interested in finding T cells or making an antibody against, for example an extra cellular domain that is required for activation of your protein, then you'd be better off taking a targeted approach.

This can only be done when you know the structure and other properties of your protein of interest.

Another example is if you'd want to make an antibody to use in, say, western blotting that can recognize homologues of your protein across multiple species. Instead of filtering/screening your polyclonal antibodies so that you have the desired clone(s) that recognizes all your species of interest, you could just find a region of homology by design and use that as a peptide.

Finally, you make a good point about glycosylation being an important component of an antigen. However, for target specificity, glycosylation can often lead to a polyclonal response that has a lot of "background" binding. Again, depends on the protein of interest.

This is a good discussion point, but not something with a finite answer - both peptides and native proteins are useful, depending on your experimental aim.

Native antigens are inherently polyvalent. Meaning, multiple terminal epitopes (structural moieties; peptidic parts) may produce antigenic response in a host. During antibody production, target is not only to achieve sensitivity but also specificity. Specificity is of supreme importance to avoid down stream false positivity issues. In order to achieve that, specific antigenic fragments (epitopes, peptides) are offered to the host instead of whole native antigen. Whole antigen may produce sensitive antibodies which are normally broadly specific.

Native antigens need rigorous purification to make them good for specific immune responses otherwise they are equally immunogenic

A lot of AUTOantibodies greatly prefer native target molecules to unfolded subunits or peptides -- esp autoAbs against cell surface receptors/ or multi-chain molecules.