All the driver does is connect your code to the database, so the driver doesn't have a huge impact unless it's very badly written and from what I've seen in well-written benchmarks, node's MySQL driver is not an Olympic Gold Medalist, but it's far from terrible - you can run 1000s of queries and maybe be a fraction of a fraction of a second slower / faster than another language after completing those 1000s of queries. From what I've seen in node-mysql, it uses callbacks in any case, so your code won't be any less performant than PHP which also has a single thread to play with.
Where you will score a fair amount of performance is in using connection pools that keeps a set amount of connections open and re-uses them since that will get rid of any latency in opening up connections which in theory should make it somewhat faster than PHP and closer to the type of performance you'd get with Java (also using a connection pool), but Java will probably still outperform it marginally due to having concurrency that allows it to handle more throughput - so to match Java's throughput in theory, you'll need to deploy at least one NodeJS instance per CPU core.
MSSQL's NodeJS driver seems very similar to its MySQL cousin also using a callback to deliver the data asynchronously, so in theory you should get similar performance. Your performance bottleneck will not be in your code, but in how fast your database can respond to the queries.
With regards to batch statements, from what I can see in examples. they're all designed to run single queries and return single results; somewhere somebody has probably created some mechanism to do batch statements, but this is not often a requirement that somebody must be able to run batch statements - you can however batch a bunch of queries doing SELECT ((query1), (query2), (query3)) or using the UNION operator to concatenate the results of multiple queries which should work for Node's way of returning results.
With regards to the databases themselves, they're all very capable databases. I prefer using MySQL although for the last project I've done which is going live in a few weeks time, it's running on MSSQL - I'm not a fan of Microsoft that much due to the legacy Steve Balmer left, but in all fairness, MSSQL handles everything I throw at it just as well as MySQL.
Disclosure, I'm not a NodeJS user and not really a fan of JavaScript crossing the browser barrier, but I have taught developers how to use NodeJS after they requested that I help them work through the docs - so my answer is based on experience in other languages and understanding how NodeJS was built, but not from using it myself.
Hope that helps?
Jan Vladimir Mostert
Idea Incubator