What do you think what are the advantages and disadvantages (of both)? Of course appart from fact that open source software is free to use. I mean rather somethink like capabilities, functionality, workload to GIS servers, easy to use etc.
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I personally favor Open Source Software, and lucky enough to work for an Open Source based company. In the past year, I've worked with a large veriety of open source GIS tools (mainly PostgreSQL, PostGIS, QGis. Ubuntu, Lighttpd and Python), and I favor them over any propietry tool in the market. Anyway, here's my 50 cents:
Open Source GIS Infrastructure
Propietry GIS Infrastructure
Apart of the aforementioned disadvantages (cost, difficult scalability, restrictions, allows little or no trial period and uncustomizable):
I think that your question is too vague to start talking about individual capabilities, but there are two things that come to my mind in general:
Scalability - If you write that 'killer app' and a lot of people start using it, all of a sudden, your initial server/database setup is overloaded. If you are using OpenSource software, you can switch over to a more powerful server or add a second server behind a load balancer. If you are paying licenses based on the number of cores or the number of users hitting the app, you are looking at a significant increase in license costs. Ever hear of anyone buying less capable servers because their licensing only allowed two cores?...
Controlling your own fate - Ever had a software bug that you couldn't get the company to acknowledge and then when the did verify it, they kept promising to fix it in the next release? If you discover a bug in most OpenSource products, you can fix it yourself or pay someone else to fix it if it is a priority. As soon as the bug is fixed, you can use the new version instead of having to wait for an official release.
I have mixed opinions our IT people have some reservations about using opensource products as some (not all) can appear one day and be gone the next.
I have played with both Opensource (MapGuide) and Proprietry (Bentley Geo Web Publisher) while I have found the Proprietry software to be a great start point and quick to get your project up and running, I found developing for that particular software a nightmare, slow to get help, small community.... and you'll pay through the teeth to get something fixed.
On the other hand MapGuide took a while to get my data into a format that it would recognize (bad data management on our side prevented some export operations).
But once in MapGuide the community is very active and very large and the api/sdk is easy to write applications for. I wouldn't look back and I'm sure many other opensource projects are similar.
Dunno If this helps but it's my personal experience.
Im def biased towards ESRI, for the main reason that with a server license, I have so many platforms available to create some really great looking apps:
Im sure there are some open source contenders, but IMO, although platforms like OpenLayers are great, they dont come near the ERSI APIs.
I also think taking advantage of functionality like Geoprocessing, Geocoding, time-aware layers, editing and even printing, with ArcGIS Server I would argue that it is ahead of the rest (admittedly at a price).
I would also argue the amount of freely avilable resources to learn, get support, watch videos, download code, etc, I would say ESRIs website is on par with MSDN for self development purposes.