Well, for example, let's compare the i7-5960X and the 5820K (I know they're not cross-platform, but whatever).
The 5960X has eight cores, but the 5820K has 6 (I believe). To compensate, the 5820K has a higher clock speed, and consequently, it's faster (at least in gaming). If the i3 has, say 2.8 GHz, the i3 kinda has a slight advantage on that.
point is both those CPUs are better for different things so you CANNOT recommend the i3 over the Pentium unless you know what he will be doing.
Also, EXACTLY what you just said applies to your previous comment about 2011 CPUs. They have different per-core performance, so your comment about clock speed is not only wrong, but incorrect fundamentally. Sorry.
I have a similar situation and question, but one has a more RAM. Similar computers, similar prices.
Pentium N3540 2.16GHz 8gb RAM 1TB HD vs.
Intel Core i3-4005U 1.70GHz 6gb RAM 500gb HD
Saying that I can suffice with the 500gb HD, which would be faster, taking into account the greater RAM in the Pentium.
I surf the internet, watch videos, play casual games with some fancy graphics, and most importantly do heavy image editing (though not with monster Photoshop; I use lots of freeware clones.) I currently have an old Duo Core, 4gb, 150gb hd. Running up on hard drive limits and freezing on games and some videos. Sometimes slow on very large image files. Which option would work better for me? Thanks!