Yes, in your example of a 50 GB vs. 1 TB/500 GB drive, the larger drive will perform significantly faster than the smaller drive, assuming you are talking about inexpensive magnetic platter disks (i.e., not a SSD). More on that later.
For the best balance of capacity and performance, I'd suggest getting a smallish SSD for around a hundred bucks for your boot drive, and a 1.5 TB or larger standard hard drive (magnetic, non-SSD) for around $70. You can find some pretty low prices on both types of storage if you watch SlickDeals.
Now, getting back to your standard (non-SSD) hard drives: first, the larger drive has a much higher areal density and probably has a much larger cache. A higher areal density means more data is packed into the same physical space--so for each rotation of the disk platter, the read/write head reads or writes more data. Assuming adequate free space on both disks, the higher areal density also means that the head won't have to travel as far when seeking to read or write the next chunk from a large stream of data.
In addition, the larger drive is probably more modern and supports a faster data transfer interface (i.e., PATA for the 50 GB drive, vs. SATA2 for the 500+ GB drive), as well as performance optimizations such as Native Command Queueing.
As some of the others have suggested, you can partition the drive to separate your OS and data, but partitioning won't necessarily give you any performance benefit. I'd say these are the primary advantages of partitioning:
- less downtime when you have to run chkdsk /f or chkdsk /r on C:
- better organization of your files (I suppose this depends on your personal preferences)
- ability to shield your OS from having all the free space consumed by other applications (e.g., preventing your DVR software from completely filling up C:\ and dragging down your system performance)
As dag pointed out, if performance trumps cost, a SSD should outperform both the small and large magnetic disks. The only catch is that SSDs do have a limited number of writes, but you can mitigate this problem by buying one large enough that you'll never come close to filling it (say, keep 20 GB or so free). This will allow the SSD's write leveling algorithms to distribute writes across the free space, so the drive should last longer.