Notes has fallen way behind even most of the free consumer email platforms not to mention the enterprise platforms it competes with.
From an end user perspective here are some issues that Notes has:
** Notes can't search well. The default search option looks only in a single field (subject, email sender, etc.) instead of across all text in the email like you'd expect it to. Consequently it's more difficult to find something you need to.
** Composition tools are basic. Notes doesn't fully undo some actions when composing email. So often you find yourself having to start from scratch because there was some composition feature used that can't be undone. It's typography is fairly poor (almost nonexistent leading/kerning and list/bullet management) so more lengthy emails look rather unprofessional.
** Fit and finish of the desktop client shows age. Notes just looks and feels old. Icons are often small and outdated. Spellcheck has no way to ignore words that start with capital letters (like names) so it's constantly asking about first names of people I email which is annoying. Dialogues like the "Add new calendar entry" leave a lot of white space and have small difficult to use fields for important information like start/end times.
** Calendar is more difficult than other systems. For some mystifying reason Notes will not allow you to forward a calendar invite you've accepted to a colleague making it more challenging to collaborate with a dynamic team. Notes calendar doesn't play well with other systems so most often a separate verification needs to be sent to ensure the individual received the meeting invite (this is especially true of meeting updates).
** It lacks integration. It's rare these days to see any new app or system integrate with Notes so it stays very siloed where other email platforms are doing deep line of business integration (CRM, video conferencing, etc.) and social integration (facebook, twitter, slack, etc.).
** Mobile and desktop syncing issues. There are some well know issues that involve reading email ,calendar invites especially, on the mobile client (IBM Traveler) that cause them to be removed from the default views of the desktop client. Basically important email can "disappear" when using the mobile client. The mobile client also doesn't allow integration with other mobile apps so calendars, for example, can't be unified on a smart phone; the Notes calendar won't feed into any other mobile calendaring app.