There are obvious overheads using partial ones, but this is not something you should probably worry about.
Particles are files. When you perform an action without partial actions, your action "costs" 1 file (this is not entirely true, but it simplifies the explanation). If your action displays 4 partial, you end up cost 5. This means that you have 4 additional I / O, and the actual cost for each call depends on the server load, server performance, etc.
But is it worth it? In my experience, in 99% of cases, no. It should also be noted that the advantages of using partial elements in terms of code readability and maintainability are usually worth the choice.
If performance should be a key feature, you should probably look for speed and improvements elsewhere.
Remember: Ruby is not a very fast programming language, and the expressiveness of the code has always been in first place in favor of presentations. Rails implicitly accepts this convention, although the Rails team is always performance oriented (and Rails 3 is a practical demo that is always there to improve)
However, you can safely use partial ones and reduce application overhead with some kind of smart caching mechanism. For example, you can place a collection rendering in a cache block so that the visualization collection operator is executed only once, then your application will simply load 1 cache file instead of 10 un-cached partitions.
One of the most unfortunate mistakes that I made many times in the beginning was to worry about actions in the wrong way, without real tests. I remember once when I tried to delete one database query in favor of a hard coded hash, because the "cost of the query", not realizing that there was another stupid query that loaded the entire collection of the table without the include statement, which led to the launch of the second query 3 times slower.
So, if you really care about performance, you probably shouldn't avoid using particulars, but instead, make sure you use all the other features. Rails lets you scale your application.