The notion "degree of X" really requires a three-way distinction to be valid, as in degrees of length (Estonian, Saami, Dinka), nasalization (Palantla Chinantec) or breathiness (Bor Dinka). If there are only two systematic values, we say "it is" or "it isn't", and we don't have to say "how much" (degree). In the present case, it is likely that you are using one language (Bengali) to set a standard of comparison for another language.
Korean has been subject to a half century of acoustic analysis, and it is clear that there has been recent language change where /p/ et al. in Seoul Korean have become "more aspirated", over time and compared to other dialects. It is now to the point that the unaspirated stops of Seoul Korean are comparable in voice onset time to the contrastively aspirated stops of languages like Apache and Khonoma Angami (Cho & Ladefoged). Some languages have extreme degrees of aspiration, for example Navaho [k] at 45 msc vs [kʰ] at 154 msc; 28 and 128 msc respectively for the same pair in Tlingit. From that perspective, p in Korean is "somewhat aspirated" and ph is "more aspirated, compared to Bengali or other Indic languages where the phonologically unaspirated stops don't have a very long VOT at all.
What makes Korean so special is that it has a third kind of consonant, transcribed typically as pp, which is termed 'fortis; tense; glottal; geminate' – all of these seem to be appropriate descriptions of the facts. These 'tense' consonants have an even lower VOT, which is the element missing for claiming that there are "degrees of aspiration:. However, the 'tense' consonants also have some kind of glottalization associated with them, at least for older speakers. It is possible that some time in the future, the p, pp, ph contrast will develop into a three-way difference in aspiration alone, but at present, there are enough other differences associated with these consonants that we can legitimately treat the system as having two orthogonal two-way differences (aspiration versus glottalization).
In one way of looking at it, English could provide another example of three-way aspiration differences (though not contrasts). It is well-known that aspiration of voiceless stops is governed by a rule where they are aspirated in foot-initial position and not aspirated elsewhere. This is often treated as a phonological (categorial) allophonic process. However, it has also been observed that for many speakers, the contrast between "g" and "k" does not involve voicing, it involves aspiration ("g" is really unaspirated [k] and "k" is aspirated [kʰ]). Putting these two facts together, one can say that phonetically we have three aspirations states: unaspirated ("g"), lightly aspirated ("k" not in foot-initial position), and more-aspirated ("k" foot-initially as in "cap")
There are plenty of ways to reduce the significance of these aspiration differences. One can maintain that the "k" / "g" contrast is indeed one of voicing and the failure of vocal fold vibration in phonetic outputs is the result of something about phonetic implementation; or one can say that that contrast is indeed phonologically one of aspiration, but phonetic implementation amplifies the degree of aspiration of foot-initial aspirated stops.
The situation with English is different from that of Korean in that English only has two kinds of underlying consonants as opposed to three in Korean, and "what is underlying" is one definition of "phonemic". But the other definition of "phonemic" refers only to phonetic outputs and the ability to reduce two phonetic categories to one by rule, referring only to available phonetic properties and not abstract phonological ones. Because of resyllabifications (an abstract phonological process), you can actually get all three stop types in comparable contexts: "a Benny" (unaspirated), "up any" (lightly aspirated), "a penny" (most aspirated). This is typically dealt with by referring to juncture / word boundary, but junctures or boundaries are not phonetic events, they are abstract phonological units. Since I don't subscribe to the strict surface-oriented view of the concept "phoneme", I don't know whether advocates of that theory would then hold that English also has "degrees of aspiration". This handout and paper by Vaux gives an overview of relevant facts and theoretical interpretations of the matter.
