Erbil has a much larger expatriate community and you will more easily find services and products geared towards your needs. Suli by contrast has a smaller xpat community and things are slightly less available, but you can still get everything you need, and in Suli fresh produce is cheap and abundant.
Security in Erbil is taken much more seriously because there is a much greater security concern. Suli is largely unaffected by recent political events since there are so few targets for ISIS, we are so remote from the conflict, and the population is so much more homogenous, Sorani Kurd. Because of that you will find fewer checkpoints, fewer guards, etc.. here. Erbil by contrast is currently inundated with refugees, is a political and economic target associated with the international community, and has a heterogenous population of Kurds, Arabs, Turkomen and Expatriates. In Erbil you would want to stick to protected areas and not wander around after dark.
Cost of living is comparable in both places, which is to say fairly low if you cook for yourself. 100K Dinar a week provides plenty of groceries for one person. I recommend sticking to employers who provide housing, especially in Erbil where that is norm anyway because of security concerns.
My personal recommendation is to avoid Erbil at present because there's simply too much war activity being based from there. The CIA has built a large base of operations there and there have been bombing attacks there by ISIS only recently. You'd probably be safe inside a compound, but make sure the compound has nice facilities before you take anything.
