The similarity in sound is the result of two factors: overlapping phonetic inventories, and word length (which affects syllable duration). If you wanted to quantify the similarity, those would be the factors to focus on. The other part of "why" focuses not on what you are reacting to, but what causes the languages to be similar. The best explanation is that this is an areal feature. Japanese and Korean sound similar, but Korean and Khakas do too, likewise you can fold in Kazakh, Mongolian and Chukchi (possibly other languages of the area that I haven't heard). However, Chukchi doesn't sound a lot like Japanese, it sounds more like Mongolian, which sounds like Khakas, which sounds like Korean... We can rule out common genetic basic because (1) errm, Altaic isn't really a valid historical linguistic group, (2) Turkic spoken further west does not sound like related Khakas etc. and (3) Chukchi is not vaguely hypothesized to be related to Japanese.
Lack of tone would not be relevant, since Korean has tonal and non-tonal dialects and virtually all dialects of Japanese (maybe indeed all) have tone, the reduced-contrast system type most common in tone languages (as contrasted with Chinese and SE Asian languages).
A similar phenomenon exists in the Pacific Northwest, where the languages all sound alike, but they are split up into a half-dozen or more genetic groups. For some reason, in contact situations, people can easily pick up a "foreign accent" without the kind of deep linguistic contact that results in exchange of many words and morphemes.