A soon to be published Human Mutation Article suggests that Polyphen is less dependent on the multiple alignment used as input. If you are not able to produce your own alignments for your specific dataset then Polyphen could perhaps be preferred for this reason.
On the other hand, if you can produce your own alignments then SIFT might be preferable since its web UI lets you specify the alignment and with the correct alignment its results are at least comparable in accuracy to Polyphen.
Honestly, both are misleading. Unless you must annotate SNPs with them, try another approach. Check out this article. Of course, this article is mostly about clinical applications. Nevertheless, I'm currently researching some (proto)oncogenes and I can say for sure that relying in alignments in order to look for phenotipic effects is too risky. This kinf of approach totally ignores correlations among positions. They are quite common and you see in this conservative analysis.
My advice is: just search the literature about the regions that you're studyin. Most high quality SNP data with phenotypic annotation isn't present on the popular public databases. E. g. The protein menin have about 150 variants annotated in UniProt when you can find about a 1000 of them (true protein level evidence) in the specialized literature.
SIFT and Polyphen2 can say opposite thing about the same SNP. How to decide who's right? So, work a bit more to suffer a lot less!!!
-- Edit --
There are other several drawbacks in both approaches. They don't correct for parology or or redundancy. This can give much higher weight to certain alignment positions than should be. But, we know that using alignment as a proxy of purifying selection only works well for low redundancy distant species sets as pointed here. The rate of sucess of SIFT/Polyphen2 is mainly due to evident constraints in protein structure. You don't need them to assess that. A 2ndry structure prediction program with a good profile guided alignment should return very similar results in a much more transparent way.
It doesnt have to be either or. Condel integrates different outputs (like SIFT and Polyphen2). So just you can just run both and integrate them.
But sticking to your rule of using one server: From Ensembl 62 on you should be able to access directly to an integrated score of polyphen2 and sift (calculated by Condel) through their API (stated here).
Now this option is already available at Ensembl: On the webserver you can access it directly or you can query teh API yourself.
This is not true, at least not in case of PolyPhen-2. It uses PSIC conservation score which is very robust and was specifically designed with highly redundant alignments in mind. PolyPhen-2 also has options to correct for paralogs (or use clean target database for true orthologs). Benchmarks show paralogs correction actually deteriorate accuracy slightly so this option is disabled by default.
The rate of success of SIFT/Polyphen2 in mainly due to evident constraints in protein structure.
SIFT does not use any secondary structure features for its predictions.