If you are playing a Downloadable MMO you start by downloading a large file the first time you play. After that, if the game ends up becoming popular, it is highly likely there will be continual development and the distribution of regular patches. This could mean frequent downloads of new content. This is good since it means you get more game to play, but the hassles can be frustrating sometimes. This is one thing you cannot skip, as a lot of gameplay features may not work on an outdated version. A new class of creatures – check. New maps and locations – check. Simply a couple of new items for your character – check.
Browser-based MMOs on the other hand have their negative points in terms of server issues. If the game is that popular, it would require a dedicated set of servers, which may not work all smoothly every time. Each new development may mean a downtime of a few hours.
Not all Browser-based MMOs are without good graphics (see the available image from Tribal Wars). 
But those which have good graphics, may take time to load fully. Good examples of MMOs which have focus on the graphics are – Habbo Hotel, Renaissance Kingdoms, Fallen Sword, and Tribal Wars. Habbo Hotel incidentally, is famous for its dynamic graphics.
Now it’s up to you to decide what kind of MMO game you want to play. The choice is yours.
(Images taken from the respective game sites)
One other significant common difference between client-based MMOs and browser based MMOs is the business plan. Client based MMOs typically have a subscripion fee in addition to an up front fee for the client and the box. Many browser based MMOs are free to play with optional, purchaseable extras, microtransactions, or other business models that let you play for free until you decide you want something extra for the game. This is certainly something to consider when looking for an MMO to play.
In the end, both types of MMOs have their pros and cons. There are high quality, entertaining, and fun MMOs of both types. The decision ultimately comes down to the type of user experience you prefer, the type of payment plan you like, and the actual game design and features that appeal to you. It is wise to try both types of MMOs, as most people find the way they interface with the game is not nearly as important as the gameplay once you are connected.