For a little background, during the last event I claimed only "Smalls" and during the current event I have claimed only "Bigs." Both events I used about 15k points (patches) or whatever they're currently called.

When referencing the related guides,

Smalls: https://runescape.wiki/w/Event_mystery_box
Bigs: https://runescape.wiki/w/Big_event_mystery_box

even though bigs cost 2x that of smalls and only carry 5 items as opposed to 3 I believe bigs are the better option. Both will give you the medium star every time but only the large offers the chance at large sized stars/lamps/dung tokens. Another thing I noticed is that you can receive the large cash bag from bigs - even though it is not listed on the guide drop table.

This event, spending the same tokens on bigs as I did on smalls last time - I have profited substantially over previous event gains. Of course, that depends on how much you value dung tokens etc. Because I got over 100k dung tokens from 25 packages. I also gained about 500k bxp and 2m gp among those same 25 packages.

Why is the claim so popular that smalls are the better option? Just because of the 1 extra roll per 500 points? I now disagree whole heartedly.

What if you don’t have a purpose for dg tokens nor gp? Would big also mean more bxp?

I am thinking yes in general. There are a handful of large sized lamps that aren't in the small event box, but that's not "bonus xp" technically. So bxp only, it looks like they have the similar odds as far as stars. I prefer lamps over stars personally.