While continuing your research on these breeds, be sure to read about them on Great Dane & Boxer rescue group websites. Rescue groups want to find forever homes for the dogs and will be brutally honest with you about the downsides of their breeds as well as the positives. Also, rescue groups have constant, firsthand experience, many times for several years and more so the experiences are not just regarding one dog.
I know several Great Danes and Boxers personally and these breeds share many traits. Both can be very comical with great senses of humor who love to entertain people. ;)
Both do require outlets for energy but honestly, the Danes do not require much more exercise than any other active dog. They also do not consume massive amounts of dogfood as many people believe they do. It is important to feed a very high quality dog food and learn as much as you can about bloat and torsion in regards to Boxers or Danes as both are deep-chested breeds making them prone to this many times fatal occurance.
Great Danes are known to be leaners. They can easily knock someone over unintentionally and because of their size you must be careful when they get the case of the zoomies. A 150 pound dog with poor brakes can be a hazard for some people, elderly and children and even other dogs.
Danes can also clear a coffee table with their tails on one swipe so if you have precious breakables, you'll learn to elevate them considerably. You also will need to commit to lifelong training and start as early as possible to avoid raising a huge dog which can be impossible or even dangerous if allowed to develop poor manners. They can easily reach anything on counters or tables and they usually consider themselves lapdogs.
They have a booming bark and can become too territorial if not properly socialized and trained. You also will likely meet many, many people who are simply terrified of your dog based on its size. Something some new Dane owners are not prepared for. You should also consider the size of your vehicle, as funny as that may seem. If you plan to take you pet places often, he should be comfortable with enough room.
Danes are amiable, friendly if well socialized, a joy to watch and interact with, very intelligent with little grooming necessary. They would thrive on large areas to be able to get out and really stretch their legs and usually enjoy other dogs of similar size to play with.
As for some cons: They can be very prey driven as they are sighthounds so extra vigilance must be taken when out and about. They many times are driven to chase anything that runs (cats, squirrels, small dogs, etc). Their vet bills will be higher as dosages will be higher for vaccines/heartworm preventative and external parasite meds.
They are prone to hip dysplasia and bloat and orthopaedic issues. They also can be quite short-lived, many times to ten years old or less. They can drool, when/if destructive, they are VERY destructive.
Boxers share many of the same fun-loving qualities and genetic tendancies such as hip dysplasia but add in the issues which can be problematic for brachycephalatic (pushed in nosed) breeds. They are adversly affected by heat and humidity which means you will need to protect them from too much exercise and activities in these conditions. They are prone to optical issues such as early cataracts.
Boxers can be easily exciteable so early training and socializing is important (as with any dog). They enjoy people and usually enjoy playing with other dogs. Their playstyles can be rough and very physical. They are an intelligent breed and thrive on mental stimulation.
They require little grooming and are considered a medium to large breed.
Boxers can also drool and can be mouthy.
Boxers are also sometimes feared by people based on their appearance so its very important to help your dog become a friendly, well-mannered dog.
You have taken the first important step towards successful dog ownership by determining the breeds you like and that fit your lifestyle. By doing as much research as possible and acquiring your dog from a very reputable source (breed rescue, extremely reputable breeder) you will save yourself and your dog heartache down the road by making the right choice of breed AND the right choice of individual dog.
Contact rescue groups, ask questions and be realistic in your decisions.
Good luck!