I have recently come across this while researching the phonetic spelling for "love", and I have come across a website (the website) that had both traditional and modern IPA spellings (with the modern IPA spelling being lə́v and traditional being lʌv). What's the difference?
The IPA doesn't actually tell you how language sounds are to be transcribed, it tells you what the standard "meaningss" of their symbols are. The letter [ɛ] means "open-mid front unrounded vowel" and [e] means "close-mid front unrounded vowel". The linguist then decides whether a certain word in a language has a "close-mid front unrounded vowel" or a "open-mid front unrounded vowel" – that is a matter of analysis.
Schwa and wedge are in complementary distribution in English, so it is mostly arbitrary to select one vs. the other symbol in a phonemic transcription. For English, there have been certain traditional choices made for various reasons, and lʌv is the traditional choice for this particular context ("that vowel" when stressed). The same goes for the various ways of transcribing other vowel qualities including diphthongs (e vs ɛ; eɪ vs ɛj). I don't know whether anyone has done a systematic study of transcription conventions for English to see whether [eɪ] is definitively the "traditional" transcription of that phoneme. More likely, traditionality is a gradient property and [eɪ] is most traditional, followed by [ei].
The choice of an acute accent for stress is not "modern", it is non-standard.