Kansai Thru Pass or Icoca?

Hello!

Me & my friend plan on traveling to Osaka for 2 weeks. We're staying in Osaka for the majority of our stay, but we plan on taking day trips to Kyoto, Kinosaki-onsen, Kobe, and Nara. Should we buy the Kansai Thru Pass or is it better/cheaper to get the ICOCA card? Should we buy the Kansai Thru Pass for when we have to travel outside of Osaka and then buy the ICOCA card for when we stay in Osaka? Is it cheaper if I buy the one day unlimited passes than the ICOCA?

When will you travel?
You have not yet decided the details of your itinerary, right?
Which area in Osaka do you plan to stay?
For your trips to cities of Kyoto, Kobe and Nara, whether a transportation pass is good may depend on which line(s) you can choose.

Regarding the hot spring resort in Kinosaki, there are several hot spring facilities accepting day trippers, but I suppose staying overnight there is worth considering.

A Kansai WIDE Area Pass of JR-West (sold at 7200 yen, valid for 4 consecutive days) pays off in your roundtrip from Shin-Osaka / Kyoto to Kinosaki-onsen taking Ltd. Express trains Konotori / Kinosaki without seat reservation.
: When you reserve a seat in a Konotori / Kinosaki, this pass does not cover the Ltd. Express charge, which can be 2050 to 2450 yen per way.
: I suppose these Ltd. Express trains do not get easily packed except in busy seasons.
: You can use this pass on JR-West lines in your trips to Kinosaki and cities of Kyoto, Kobe and Nara if you make the trips within 4 consecutive days.
http://www.japan-guide.com/e/e2361_08.html

A 2-day / 3-day Kansai Thru Pass, which is a transportation pass for non-JR lines, can be used on non-consecutive days.
: Kinosaki is outside the valid area of this pass.
: Non-JR bus and railroad (including subway) lines can be useful or inevitable in traveling inside cities of Osaka, Kyoto, Kobe and Nara.
: This pass does not easily pay off if you do not use it to travel between or among the cities.

Should we buy the Kansai Thru Pass for when we have to travel outside of Osaka?

That may be a good choice if you mainly use non-JR lines in trips to cities of Kyoto, Kobe and Nara.

is it better/cheaper to get the ICOCA card?

An ICOCA Card is not a discount pass. It does not give you a discount in particular but it can save your time and trouble for handling cash and paper tickets.
An ICOCA Card can be accepted on many bus and railroad (including subway) lines in cities of Osaka, Kyoto, Kobe and Nara, except on Kyoto City Bus lines, Eizan Electric Railway lines and JR Shinkansen lines.
http://www.japan-guide.com/e/e2359_003.html

Is it cheaper if I buy the one day unlimited passes?

Regarding a 1-day / 2-day Osaka Amazing Pass (renamed from "Osaka Unlimited Pass"), I suppose whether it pays off depends on places to visit and traveling paces.
The same I suppose regarding a Kyoto Sightseeing One-day / Two-day Pass Card.
A Kyoto City Bus All-day Pass sounds easier to pay off if you visit places inside the allocated flat-fare zone.
http://www.osaka-info.jp/osp/jp/index.html
http://www.city.kyoto.jp/koho/eng/access/transport.html

[From Osaka City to Kyoto / Kobe / Nara City by rail]

If you stay near Osaka Station, probably the simplest way to travel
to Kyoto City is taking a Special Rapid train on JR Kyoto Line to Kyoto Station /
to Kobe City is taking a Special Rapid train on JR Kobe Line to Sannomiya Station /
to Kobe City is taking a Miyakoji Rapid train on (JR) Nara Line to Nara Station.

If you stay in Namba area, you can choose
lines of Kintetsu to travel from Osaka-Namba to Kyoto (though it�fs a little roundabout) /
lines of Hanshin to travel from Osaka-Namba to Kobe-Sannomiya /
a line of Kintetsu to travel from Osaka-Namba to Kintetsu-Nara.