new to macs- processor vs windows?

Yes, it will be faster. You will be surprised at the performance improvement.

I went from a 2.8 Pentium 4 to a 1.83 Core 1 Duo and was expecting a sluggish, dragging system. I was very happy.

 

The core2duo processor in the mini is MUCH more powerful than your current Pentium 4. They have completely different architectures (not to mention the mini has two processors instead of the one of the Pentium 4) so you can't compare them directly using only their clock speed.

Yeah, it's a little confusing, but the bottom line is that you'll be getting a major upgrade with the mini.

 

The thing is, in the Pentium 4 era, Intel's marketing department went all-in on the "Mhz battle", implying that larger numbers equaled a faster computer. This isn't the case, and they effectively hit a dead end with the Pentium 4, where they had huge Mhz numbers but really weren't very fast at all. There's a reason Intel itself ditched the line and went with the Core architecture used in Macs today--it's just plain faster in almost every measurable way, both Mhz-for-Mhz and in absolute terms. (There's also a reason that Apple switched from the PPC to Intel chips only AFTER Core processors started shipping.)

Among other things, the mini you're looking at has a drastically faster system bus than your old Pentium 4, which would make it somewhat faster even if the processors were equivalent. The mini also effectively has two processors instead of one, which can make it anywhere from a little to twice as fast as a comparable single-processor machine.

Synthetic benchmarks aren't a very good way of measuring the speed of a computer, but if you want numbers for the sake of comparison for the processors themselves, have a look at this website:
http://www.cpubenchmark.net/cpu_list.php

...where you will see a Pentium 4 2.6GHz score a 409 on their benchmark, where a Core2 Duo P7550 2.26GHz, which is what the mini uses, scores 1668--over four times faster. So, if it only had one core instead of two, it would still be twice as fast (in fact, you can find a Core2 Solo 1.4GHz on that list, which is only a single processor; it scores 483, still faster than a 2.6GHz P4).

So there you go.

Incidentally, if you're shopping for a mini, I'd seriously consider the 2nd-tier mini--the extra money gets you a 10% faster processor, maxed out RAM, and a bigger hard drive, without the hassles of physically upgrading it yourself. My dad just bought one, and he loves it.